When House hands Foreman the bone saw, the cord is draped over the patient, in the next shot when Foreman is making the cuts, the cord is under the table.
Foreman begins an autopsy by cutting through the chest using an electric circular bone saw. This saw will not cut through bare skin. It's actually rather similar to the saws used to cut casts. The saw basically uses friction to cut through bone, but it is pretty harmless to skin. The way to cut through skin is with a scalpel.
Chase's scene in church is inaccurate. It is against Catholic canon law for a priest to give absolution contingent on the penitent turning himself in to the authorities. This holds even if non-performance of that penance would somehow result in the death of the priest.
House decides that the patient needs to be put on the drug carbamazepine, Aka Tegretol, and tells Chase to administer it. When you next see Chase in the room with the patient hes hanging an IV bag. Tegretol is not available in an injection form.
When Chase is up and getting ready to give news of Donny's death, Cameron tells Chase that it's 4am, but the windows show that it is much later.